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|Title||On Codes over the Rings Fq + uFq + vFq + uvFq|
Codes over finite rings have been studied in the early 1970’s . A great deal of attention has been given to codes over finite rings from 1990 , because of their new role in algebraic coding theory and their successful applications. In previous studies, some authors determined the structure of the ring F2 + uF2 + vF2 + uvF2, where u2 = v2 = 0 and uv = vu, also they obtained linear codes, self dual codes, cyclic codes, and consta-cyclic codes over this ring as in ,,,. In this thesis, we aim to generalize the previous studies from the ring F2+uF2+vF2+uvF2 to the ring Fq + uFq + vFq + uvFq, where q is a power of the prime p and u2 = v2 = 0 uv = vu, so we obtain the linear codes over R = Fq + uFq + vFq + uvFq, then we investigate self dual codes over R and we find that it can be generalized only when q is a power of the prime 2, also we obtain cyclic and consta-cyclic codes over R, and we generalize the Gray map used for codes over F2 + uF2 + vF2 + uvF2, finally we obtain another gray map for codes over R.
|Publisher||الجامعة الإسلامية - غزة|
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